Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions

B.M. Mohan, S.K. Kar

October 24, 2012 by CRC Press
Reference - 247 Pages - 66 B/W Illustrations
ISBN 9781466517295 - CAT# K15099


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  • Summarizes key developments in area of orthogonal functions in optimal control and state estimation
  • Focuses on development of recursive algorithms
  • Discusses optimal control of varieties of systems e.g. linear/non-linear, singular, large scale systems, and more
  • Includes descriptions of both recursive and non-recursive algorithms
  • Describes Block pulse functions and Legendre polynomials


Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional.

This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria.

Illustrated throughout with detailed examples, the book covers topics including:

  • Block-pulse functions and shifted Legendre polynomials
  • State estimation of linear time-invariant systems
  • Linear optimal control systems incorporating observers
  • Optimal control of systems described by integro-differential equations
  • Linear-quadratic-Gaussian control
  • Optimal control of singular systems
  • Optimal control of time-delay systems with and without reverse time terms
  • Optimal control of second-order nonlinear systems
  • Hierarchical control of linear time-invariant and time-varying systems